A Characterization of $P_6$-Free Irredundance Perfect Graphs

Abstract

Let $ir(G)$ and $\gamma(G)$ be the irredundance number and the domination number of a graph $G$, respectively. A graph $G$ is called irredundance perfect if $ir(H)=\gamma(H)$ for every induced subgraph $H$ of $G$. The subclass of $P_6$-free irredundance perfect graphs has been studied extensively. In this paper, we present a characterization of this graph class in terms of eleven forbidden induced subgraphs.